Graph scale-space theory for distributed peak and pit identification

Andreas Loukas, Marco Cattani, Marco Zuniga, Jie Gao

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

6 Citations (Scopus)


Graph filters are a recent and powerful tool to process information in graphs. Yet despite their advantages, graph filters are limited. The limitation is exposed in a filtering task that is common, but not fully solved in sensor networks: the identification of a signal's peaks and pits. Choosing the correct filter necessitates a-priori information about the signal and the network topology. Furthermore, in sparse and irregular networks graph filters introduce distortion, effectively rendering identification inaccurate, even when signal-specific information is available. Motivated by the need for a multi-scale approach, this paper extends classical results on scale-space analysis to graphs. We derive the family of scale-space kernels (or filters) that are suitable for graphs and show how these can be used to observe a signal at all possible scales: from fine to coarse. The gathered information is then used to distributedly identify the signal's peaks and pits. Our graph scale-space approach diminishes the need for a-priori knowledge, and reduces the effects caused by noise, sparse and irregular topologies, exhibiting: (i) superior resilience to noise than the state-of-the-art, and (ii) at least 20% higher precision than the best graph filter, when evaluated on our testbed.
Original languageEnglish
Title of host publicationIPSN '15
Subtitle of host publicationProceedings of the 14th International Conference on Information Processing in Sensor Networks
Place of PublicationNew York, NY
PublisherAssociation for Computing Machinery (ACM)
Number of pages12
ISBN (Print)978-1-4503-3475-4
Publication statusPublished - 13 Apr 2015
EventIPSN 2015: 14th International Symposium on Information Processing in Sensor Networks - Seattle, United States
Duration: 13 Apr 201516 Apr 2015
Conference number: 14th


ConferenceIPSN 2015
CountryUnited States


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